The British rivals were due to face each other earlier this year but Fury vacated the British and Commonwealth belts after failing to agree terms and the pair have become embroiled in a war of words in recent months.
Price has since secured the two titles and will defend them against Matt Skelton on Saturday, while Fury is fighting on the same night against former world title challenger Kevin Johnson.
Liverpudlian Price admits both he and Fury have benefitted from their close rivalry and is hopeful the bout will take place within six months if they remain unbeaten.
"If the fight can happen, me and Tyson Fury are lucky to have each other," he told The Liverpool Echo.
"We are arch rivals, we're both from the north west of England, we fought as amateurs and you couldn't write it better. We are both giant men and are fortunate to have that rivalry. Not just from a business sense but also for motivation.
"It could, genuinely happen, maybe in July next year.
"We are going to have to sit round a negotiating table and come to terms with how the business of the fight is going to be dealt with.
"I know I would want Frank Maloney to promote the fight, because it will be better business for me, or even for it to be a joint promotion so that I still get my share.
"At the end of day, without me and Tyson Fury, the fight would not be happening so we deserve the lion's share. So we're all going to have to sit round the table and get the best out of it."
Price has a begrudging respect for Fury and is happy for him to continue his verbal assault if it continues to publicise a future fight.
"As far as building that fight, I'm happy to let him keep talking. His words are exactly that - just words. And they don't bother me in the slightest but they are getting people interested in the fight," he said.
"I bring people to the fights because of my boxing ability and punching power but he brings people because he's a bit of a comedian.
"But I also accept that he is a good fighter as well so it's a good fight, if it can be made."